What does it mean to be "correct" in pronunciation or grammar?

The problem is that the terms correct and incorrect are used in situations where non-standard, unusual or unlikely would be better descriptions.

Double negatives are non-standard but "correct" in certain dialects. The phrase a strong smoker is an unusual collocation (cf. a heavy smoker), but can hardly said to be incorrect. How have you got that black eye? is an unlikely sentence, but again cannot said to be incorrect.

Nevertheless, the term incorrect can be applied to large areas of grammar. It is simply incorrect to say: Understand do I you not or She has two dog or I will play football yesterday.

There's a case for saying that the authority in these cases is the grammatical hard-wiring that would lead every native English speaker to reject such formulations.

I find the words correct and incorrect to be inadequate terms in the discussion of language. I try to limit them myself to what is spoken by infants and foreign learners before they become competent. I find it much more helpful to think in terms of whether a piece of discourse achieves the purpose the speaker or writer has in mind. The language used will vary according to time and place, and it will also vary according to the topic under discussion, the relationship between those involved and the means of communication. (For the linguistically minded, that's a very crude attempt to put into simple terms Michael Halliday's concepts of field, tenor and mode.)

If I may crave indulgence, I have written elsewhere on this topic. Here's the final paragraph:

When I read a sentence I ask not so much, ‘Is it correct?’ but, ‘Do I want to read any more of this stuff?’ ‘Getting it right’ means successfully using language to achieve the purpose intended, not necessarily complying with a set of rules. Achieving the purpose intended includes producing a sympathetic response in our readers. Placing the emphasis on effectiveness rather than correctness seems to me more likely to produce the desired result. The alternative seems to suppose that once you have complied with the rules laid down by this or that authority you have done all you need to. That is far from the truth.

As @Barrie implies, the words correct and incorrect are often misused in the context of language use. And in fact they're far more likely to be used by pedagogues and grammarians (prescriptivists) than by linguists (descriptivists).

Having said that, there are plenty of usages that most/all competent speakers would agree are "incorrect" - even if people do use them, and others understand them perfectly well. For example, few would defend Pink Floyd's We Don't Need No Education as "correct" use of English. But we all understand what it means, and most of us get the "joke".

To specifically address OP's question as to who decides what constitutes "correct" usage?, I think the answer is simply that it's a consensus of many different groups. Or not, oftentimes, since even here on EL&U we often see unresolved disagreements on such matters. Though my own impression is that on average the site leans towards tolerant descriptivism rather than endless appeals to "authorities" which are often somewhat behind the times.